A. Plankensteiner, P. Rödhammer
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Finite Element Analysis of X-Ray Targets
Arno Plankensteiner, Peter Rödhammer
Technology Center, Plansee AG, Reutte, Austria
Summary
Over the last decades the demand for higher X-ray doses in novel diagnostic
procedures based on medical computer tomography has led to larger and more
complex designs of X-ray targets. In the present work the limits to up-scaling of
present-day designs using the present standard materials are analyzed using Finite
Element Analysis (FEA). The commercial FEM package ABAQUS/Standard V6.5 was
employed. Simulations were based on an axi-symmetric model and an elastic-plastic
material law for the metallic components. X-ray targets with diameter 190mm (T190)
and 250mm (T250) operated at 150Hz and 250Hz were analyzed. Exposures of
100kW/10sec and 100kW/30sec were chosen to represent potential future
requirements.
According to the results of the present FEA the scale-up of present designs of X-ray
targets using TZM as base material may be expected to reach its limits at diameters of
~ 250mm and at ratings equivalent to 100kW/10sec exposures. It is concluded that
novel materials with mechanical properties improved markedly beyond those of TZM,
combined with novel designs, are prerequisite for the rateability of X-ray targets
beyond this threshold.
Keywords
Computer tomography, X-ray anode, finite element analysis, high temperature
plasticity, molybdenum alloy, tungsten rhenium alloy, graphite
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A. Plankensteiner, P. Rödhammer
1. Introduction
Over the last three decades the demand for higher X-ray doses in novel diagnostic
procedures based on medical computer tomography has led to ever larger and more
complex designs of rotating X-ray targets. At present, anodes consisting of a
molybdenum alloy disc with a thin tungsten/rhenium layer serving as focal track and a
graphite ring brazed to its back are the state of the art in tubes for computer
tomography (CT) applications. The diameters of such anodes have increased to about
200mm, and their weight to more than 5kg. At the same time, the loads experienced in
application have increased dramatically. This applies to the combination of rotational
frequency, power density of the electron beam generating the X-ray, input of electric
energy, and the associated increase in operating temperatures. At this point in time,
the materials used for X-ray targets and technologies employed for their manufacturing
are becoming the limiting factors in satisfying the progressing needs of medical
diagnostics. In an increasing number of applications the increasing loads lead to
accelerated ageing of the W/Re focal track, to irreversible deformation or even to
failure of the metal disc and/or to debonding of the joining between metal and graphite.
In order to prevent these failures and to increase the envelope for operating
parameters there is an urgent need for improved designs, materials, and joining
technologies.
The present work is motivated by recurring reports from the field that anodes used in
advanced diagnostic techniques had failed. Post-mortem analysis showed that the
anodes had deformed and acquired an unbalance, and that in consequence the
brazing had failed between the metal cap and the graphite back.
In this paper results of a finite element analysis for X-ray anodes are presented aiming
at evaluating present and up-scaled anode designs with regard to foreseeable future
anode ratings. One aim of this analysis is to gauge the need for improvement of the
tensile properties of up-graded or novel molybdenum alloys required for present and
future diagnostic techniques in CT tomography. An axisymmetric model is adopted
throughout the calculations. The stresses in the compound metal-graphite anodes
resulting from the production history are simulated. Deformations as well as
temperature and stress/strain distributions resulting from present and anticipated future
loading conditions in tube applications are calculated.
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2. Operational requirements for CT applications
Basic requirements for X-ray anodes are highly stable radiation output and high
voltage stability over the lifetime of the tube (~105 exposures). Form stability of the
focal track and balance retention are prerequisite for image quality and bearing life,
respectively. Demanding procedures such as a CT spiral scan call for cyclic inputs of
electric energy of up to 60kW/30sec with cooling times up to 10 minutes. Rotational
frequencies for anodes with a diameter of 200mm are presently constrained to <
150Hz due to limitations in the material properties. Temperatures at the brazing
interface are designed to stay below 1400°C, with a safety margin up to 1600°C in
case of disruptions. Novel diagnostic techniques will involve considerably higher
ratings. In particular, the size of the focal spot will be reduced to < 1 x 10mm2, at power
levels < 100kW and energy inputs < 1MJ.
One answer to inadequate life of the focal track at present ratings, and much more so
at novel techniques, lies in anodes with larger diameters rotating at higher rotational
speeds. Here, an up scaling to diameters of 250mm and an increase of the rotational
frequency up to 200Hz appear feasible based on an evolution of present-day tube
technology. However, the resulting centrifugal forces will put still higher demands on
the mechanical properties of the materials used in the design of the X-ray targets. This
holds true in particular for the molybdenum alloy disc that is largely responsible for the
form stability of the compound anode.
3. Design and production aspects of X-ray anodes for CT
applications
The structural backbone of the anode is generally formed by a disk made of a
dispersion strengthened molybdenum alloy such as TZM (Mo 0.5Ti 0.08Zr 0.025C),
MHC (Mo 1Hf 0.1C) or closely related alloys [1]. A thin layer of a W/Re alloy (for CT
applications usually W10Re) serves to generate X-rays upon impact of energetic
electrons emitted from the cathode. A graphite ring is brazed to the back side of the
molybdenum disc, serving both for heat storage and for heat dissipation by radiation.
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A. Plankensteiner, P. Rödhammer
Ø250
Ø190
Fig. 1: CAD-half models representing different designs of X-ray targets: Ø190 with
Ø190mm (left) and Ø250 with Ø250mm (right).
Target Ø190 represents a typical design of metal-graphite compound X-ray anodes
used in one of the highest-rating diagnostic techniques (spiral scan computer
tomography) and target Ø250 represents a draft design for anticipated future
applications arrived at by straightforward up-scaling of target Ø190 to larger diameter
and thickness.
The metal part is usually produced by means of powder metallurgical processes in the
following sequence of steps:
•
•
•
•
•
•
Co-compacting the TZM and W/Re powders to a compound disk
Sintering
Hot forging to conical shape (overall degree of deformation is 25% to 40%)
Machining of metal cap
High temperature brazing of metal cap to graphite ring with brazing
temperatures of ~1750°C for Ti braze or ~2000°C for V/Ta/Zr braze
Attachment of a TZM shaft (see Fig. 1) by brazing (usually Ti-braze)
High temperature brazing is required in present high-end applications because
operating temperatures in the brazing interface metal-graphite may exceed 1400°C.
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4. Properties of materials used for X-ray anodes
For TZM thermo-physical and mechanical material data have been obtained on
specimens taken from anodes in the final state of production cycle, i.e. after high
temperature brazing. Comparison with data for standard TZM [2] shows that the tensile
properties of TZM are degraded in the course of the exposure to 2000°C during high
temperature brazing. The tensile data of W/Re were evaluated on a sample specially
prepared for this test under conditions comparable to those reigning during
manufacture of X-ray anodes. Generally, temperature-dependent material data are
used throughout the FEM analysis. In particular, temperature dependent stress-strain
relationships covering the full plastic range are used for TZM and W/Re. Note that
W/Re as it is present in X-ray anodes exhibits no plastic deformation below
temperatures of 1000°C. Therefore, a purely elastic behaviour is assumed for W/Re at
T < 1000°C.
Emissivity
[-]
Thermal
Conductivity
[W/(m · K)]
Specific Heat
[J/(kg · K)]
RT
RT
1400°C
RT
1400°C
Graphite
0.88
135
58
706
2020
TZM
0.22
123
89
226
356
W10Re
0.30
77
69
132
154
Table 1: Thermo-physical surface and material properties of anode grade TZM,
W10Re and graphite.
Density
3
[g/cm ]
Young’s Modulus
[GPa]
Coefficient of
Thermal Expansion
[·10-6/K]
RT
RT
1400°C
RT
1400°C
Graphite
1.82
12
12
4.4
6.1
TZM
10.15
265
187
5.4
6.1
W10Re
19.00
377
229
4.8
5.2
Table 2: Mechanical material properties of anode grade TZM, W10Re and graphite.
The graphite grade is IG610 from Toyo Tanso [3], a fine grained, high strength and
high purity grade widely used for X-ray targets. The braze material chosen is a V/Ta/Zr
braze modelled in an approximate way only by using the elasto-plastic material
properties of V and Ta.
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Temperature [°C]
Rp0.2
TZM
W10Re
RT
500
800
1000
1200
1400
1600
454
139
150
169
141
133
78
-
-
-
260
205
167
130
Table 3: Tensile yield stress Rp0.2 as a function of temperature for anode grade TZM
and W10Re.
5. Finite element based design study
The finite element analyses as well as the pre- and post-processing are performed with
the commercial FEM package ABAQUS/Standard V6.5 and ABAQUS/CAE V6.5 [4],
respectively. The initial state of the anode is defined as stress-free at the end of a
stress-relieving thermal treatment at 1350°C. The stresses building up during the
subsequent cool-down to ambient temperature act as initial stresses to the FEA of the
operation of the anode in the X-ray tube.
Centrifugal loads resulting from rotational frequencies of 150Hz and 250Hz were
applied. The power input by the electron beam was split between the focal track of
11mm width (57% of nominal power) and the thermal load by back-scattered electrons
(13% of nominal power) distributed over a fraction of the front side of the anode.
Present ratings for spiral scan CT applications range from 60kW/30s to 100kW/5s. The
rating conditions employed for the modeling of future diagnostic exposures are
100kW/10s for both the anode Ø190 and Ø250, and 100kW/30s for anode Ø250. The
latter load exceeds present exposure times (at 100kW) by a factor of 5 and is deemed
to represent the extreme of foreseeable future ratings. Only a single cycle of exposure
followed by cooling down is simulated. The cooling time was chosen as 10 minutes.
The thermal response of the targets was modelled including the different modes of
power dissipation (radiation, convection via the shaft). The temperature of the
anode/shaft assembly was set to 450°C at the start of exposure (typical conditions of
“warm start”). The temperature at the bottom surface of the shaft (heat-sinked to the
rotor) was held constant at 450°C. Radiation cooling to ambient temperature is
activated at all surfaces. The thermo-mechanical response resulting from the power
input and the centrifugal forces have been modelled based on thermo-elasto-plastic
material laws for TZM and W/Re, and on thermo-elastic material behaviour for
graphite.
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CL
CL
c)
a)
CL
b)
Fig. 2: Axisymmetric cross sections including principal dimensions of X-ray targets:
a) Ø190, b) Ø250, and c) TZM shaft.
6. Results
In the following graphical presentation of the FEA results cross sections of graphite
ring and shaft are partly omitted. Note that the following grey value coding applies to all
contour plots.
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temperature [°C]
A. Plankensteiner, P. Rödhammer
von Mises stress [MPa]
equiv. plastic strain [-]
6.1. Initial cooling down and rotational loading
For anodes Ø190 and Ø250 calculated von Mises stress distributions are shown below
for the end of the initial cooling down procedure (Fig. 3) and subsequentially
superposed rotational loading (Fig. 4) as described in section 5.
Ø250
CD
Ø190
Fig. 3: Distribution of the initial von Mises stress for targets Ø190 and Ø250 at RT after
cooling down (CD) from 1350°C.
Ø250
250Hz 150Hz
Ø190
Fig. 4: Distribution of the von Mises stress for targets Ø190 and Ø250 at RT for
rotational frequencies of 150Hz and 250Hz (superposed onto the initial stress state by
cooling down).
6.2. Thermal response to exposure
For anodes Ø190 and Ø250 the calculated temperature distributions at the end of
exposure (Fig. 5) as well as temporal evolutions of the temperature at the focal track
(Fig. 6) are shown in the following.
A. Plankensteiner, P. Rödhammer
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Ø250
100kW/30s
100kW/10s
Ø190
Fig. 5: Targets Ø190 and Ø250: Temperature distributions at the end of the exposure.
Ø250mm,
100kW/30s
Ø190mm,
100kW/10s
Ø250mm,
100kW/10s
Fig. 6: Evolution of the temperatures at the focal track for targets T190 and T250 for
100kW/10s and 100kW/30s, respectively.
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6.3. Stresses, strains and displacements due to exposure
The temperature distribution at the end of exposure and end of cooling down
subsequent to the exposure, respectively, was the basis for the evaluation of stresses,
strains and displacements as presented below.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 7: Distribution of the von Mises stress for target Ø190 for 150Hz / 250Hz and
100kW/10s at the end of the exposure.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 8: Distribution of the von Mises stress for target Ø250 for 150Hz / 250Hz and
100kW/10s / 100kW/30s at the end of the exposure.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 9: Distribution of the von Mises stress for target Ø190 for 150Hz / 250Hz and
100kW/10s at the end of cooling down after the exposure.
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100kW/30s
250Hz 150Hz
100kW/10s
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Fig. 10: Distribution of the von Mises stress for target Ø250 for 150Hz / 250Hz and
100kW/10s / 100kW/30s at the end of cooling down after the exposure.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 11: Distribution of the equivalent plastic strain for target Ø190 for 150Hz / 250Hz
and 100kW/10s at the end of the exposure.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 12: Distribution of the equivalent plastic strain for target Ø250 for 150Hz / 250Hz
and 100kW/10s / 100kW/30s at the end of the exposure.
100kW/30s
250Hz 150Hz
100kW/10s
Fig. 13: Distribution of the equivalent plastic strain for target Ø190 for 150Hz / 250Hz
and 100kW/10s at the end of cooling down after the exposure.
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100kW/30s
250Hz 150Hz
100kW/10s
A. Plankensteiner, P. Rödhammer
Fig. 14: Distribution of the equivalent plastic strain for target Ø250 for 150Hz / 250Hz
and 100kW/10s /100kW/30s at the end of cooling down after the exposure.
Ø250mm, 250Hz,
100kW / 30s
Ø190mm, 150Hz,
100kW / 10s
Ø250mm, 250Hz,
100kW / 30s
Ø190mm, 150Hz,
100kW / 10s
Fig. 15: Evolution of the displacement at the outer diameter of targets Ø190 and Ø250
for load of 100kW/10s/150Hz and 100kW/30s/250Hz. Loading sequences are: t=0s-1s:
isothermal cooling down to RT from 1350°C, t=1s-2s: spinning, t=2s-3s: isothermal
heating to 450°C, t=3s-33(13)s: electron beam exposure (transient), t=33(13)s633(613)s: cooling down for 10 minutes (transient).
7. Discussion
The initial (von Mises) stress resulting from cool-down of the target from final heat
treatment at 1350°C to room temperature (see Fig.3) lies in an uncritical range of
100MPa for both target types.
By spinning the targets up to a rotational frequency of 250Hz high stress levels at the
inner diameter of the targets are generated, in the range of 250MPa for the target with
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250mm diameter (see Fig.4). These stresses cause plastic strains at the inner
diameter of T250 that lie in the same range as those obtained under electron beam
exposure (see Fig.12). Note that the criticality of increased rotational frequencies is
borne out already at present designs and loading conditions, with a dramatic increase
in failure rates during tube operation being observed upon an increase of the rotational
frequency e.g. from 120Hz to 150Hz.
The evolution of the focal temperatures (= 2D-averaged surface temperature at the
midpoint of the track width) under an electron beam exposure of 100kW is shown in
Fig.6. The maximum of ~1750°C attained after 10 sec (for T190) and after 30 sec (for
T250) is compatible with the temperature spike in the focal spot to be superposed.
During the 600 sec pause time (not shown) the anodes cool down to starting
temperatures of 500 – 600°C. In cyclic operation final temperatures may be expected
to reach an upper limit around 1900°C. As obvious from Fig.6 anode T250 holds a
large temperature threshold when operated at 100kW/10sec cycles.
The cross-sectional distributions of temperatures (Fig.5) show pronounced
temperature gradients between the hot outer section and the cooler inner section. For
T250 the gradient appears steeper after the 10sec exposure than after the 30sec
exposure. As discussed below, these gradients induce severe radial stresses in the
target via differential thermal expansion.
At the end of exposure superposition of centrifugal forces and temperature-induced
stresses generate stress levels that in some areas of the cross-section are well beyond
the yield strength at the respective temperatures (see Figs. 8 and 9). In particular the
area around the inner radius is put under severe tensile stress under the pulling action
of the hot outer ring. As to be expected the situation is most critical for target T250
operating at 250Hz. Note that local stress levels might be even higher in transient
states with more unfavourable temperature distributions (e.g. steeper gradients).
During cool-down the outer region of the anodes goes into a state of tensile stress (see
Figs. 9 and 10). Below the focal track stresses in the TZM rise up to the range of
250MPa, discomfortingly high in view of the thermo-shock loading of the focal track
and possible crack formation in the latter.
At the end of exposure plastic straining has occurred for both designs and under all
loading conditions (see Figs. 11 and 12). The accumulated plastic strains are on the
order of 1%, and for a given design are increasing with frequency and exposure time.
Additional plastic straining occurs during cool-down of the anodes in the outer regions,
whereas the inner section remains unaffected (see Figs. 13 and 14).
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8. Conclusions
Keeping in mind that the elastic-plastic material behaviour employed in the present
model calculations does not account for creep, and that no material fatigue has been
considered, the following conclusions have to be regarded as preliminary.
For 100kW/10sec exposures an X-ray target based on design T190 and operated at
250Hz (as required by focal spot temperatures) would be critical with regard to stress
levels and deformations. Target T250 driven at 150Hz could be operated at acceptable
temperature levels both at focal spot and brazing interface, as well as at stress levels
compatible with TZM. However plastic deformation will occur, so the joining to the
graphite back will have to be designed to tolerate deformations of the TZM part in the
order of some tenths of a percent. Focal track degradation under these loading
conditions remains to be evaluated.
For the limiting case of 100kW exposures of 30 sec
250mm diameter and its higher heat storage comes
already the operation at 150Hz would lead to stresses
deemed to be in excess of safe operational conditions,
and fracture probability.
duration only the target with
into consideration. However,
and plastic strains which are
in view of plastic deformation
In summary the scale-up of present designs of X-ray targets using present standard
materials such as TZM may be expected to reach its limits at diameters of ≤ 250mm
and at ratings comparable to 100kW/10sec exposures. Novel materials with properties
such as hot strength, ductility and high-cycle fatigue improved significantly beyond
those of TZM, and novel designs are prerequisite for rateability of X-ray targets beyond
this threshold.
References
[1]
J. Warren, G. Reznikov, in Proc. 15th Int. Plansee Seminar (eds. G. Kneringer et
al.), Reutte, Austria, 2001, Vol. 4, 79-96.
[2]
Ermittlung der mechanischen Eigenschaften an verschiedenen DrehanodenTZM-Varianten (in German), Technical Report TZ2755, Plansee AG, 2005.
[3]
Isotropic Graphite Grades Product Brochure, TOYO TANSO CO., LTD., Tokyo,
Japan, 2005.
[4]
ABAQUS V6.5, ABAQUS, Inc., Providence, RI, 2005.